Sequences & Series Questions and Answers

8 points Factor f x 6x 13x 14x 3 into linear factors given that k 3 is a zero of the function Hint If x k is a zero then x k is a factor

For the given functions a express dw dt at the given value of t w z sin xy x 2t y In t 5 z e 4 t 4 a Express dw dw dt dw as a function of t both by using the Chain Rule and by expressing w in terms of t and differentiating directly with respect to t Then b evaluate dt as a function of t

f x 2x4 2x 3x 1x 22 Give your list in increasing order Beside each possible rational root type yes if it is a root and no if it is not a root Leave any unnecessary answer blanks empty Possible rational root Possible rational root Possible rational root Possible rational root Possible rational root Possible rational root Possible rational root Possible rational root Possible rational root Is it a root Is it a root Is it a root Is it a root Is it a root Is it a root Is it a root Is it a root Is it a root

Simplify by rationalizing the denominator 2 6x 2 6x Simplify your answer Type an exact answer using radicals as

Combine 4 112 28 Next question 4 112 28 Type an exact answer using radicals as needed Simplify your answer

Simplify 16x24 20 20 16x 4 2 y

Simplify Express the answer with positive exponents 1 3 a a 2 15 2 15 1 a 3 Simplify your answer Use integers or fractions for any numbers in the expression

N a 12 C d The Fourier series of the function f x e NHNG 14 2 Bo b rak 14 1 2 0 0 a at the point e 0 converges to the value

Write a recursive formula for the geometric sequence 40 20 10 a an an

Solve the equation Write the solution set with the exact values given in terms of common or natural logarithms Also give approximate solutions to 4 decimal places if necessary log 6 13 1 log 4 Part 0 5 Part 1 of 5 Isolate the logarithms on one side of the equation

Given that f x 2 3x 6x Find the difference quotient f x h f x h 9 where h 0

Let a represent the hourly wage for the electrician Let p represent the hourly wage for the plumber There are two unknown quantities We will set up a system of two independent equations relating a and p Average hourly wage of the electrician and plumber 9 2 Therefore 9 hr S 5 hr SP 5 548 hr 40 40 X 5

Verify each identity sec 2 xcot 2 x 1 cot 2x

tanxcsc2x tanx cotx To verify the identity start with the more complicated side and transform it to look like the other side Choose the correct transformations and transform the expression at each step tan x csc 2x tanx tan x nx Do not simplify tanx csc x tanx cotx To verify the identity start with the more complicated side and transform it to look like the other side Choose the correct transformations and transform the expression at each step

Partners are building a clothing business on Amazon and looking for manufacturers to sew their clothing They found two options they like Company A has a one time introductory fee of 1745 that charges 4 per item to manufacture Company B is an in home program which charges 547 to enroll and then 13 per item to manufacture Though Company B is cheaper at first how many items must be manufactured before the total cost of Company A matches the total cost of the Company B manufacturer The total cost of both the Companies will be the same after approximately manufactured Type a whole number Round decimal answers to the nearest week The total amount paid for that many clothing items will be decimal answers to the nearest dollar items are Type a whole number Round

In one class homework is worth 15 of the final grade each of 3 projects is worth 20 and a final exam is worth 25 a If a student has an 82 homework average and a 96 on the first project what is the student s grade at this point b If the same student from part a gets a 77 on the second project and a 73 on the third project what is the lowest grade the student can get on the final exam to get an 80 overall in the cou a The grade at this point is Simplify your answer Round to the nearest tenth as needed b The lowest possible grade is 0 C

The graph of the boundary equations for the system of inequalities is shown with the system 2x 8y 120 6x 3y 150 y Xx y 0 0 2x 8y 120 Locate the solution region y 6x 3y 150 6x 3y 150 6x 3y 150

Evaluate each logarithm by using properties of logarithms and the following facts log x 5 2 loga y 1 6 loga z 2 3 a log xy b loga 1 c log x4 d loga y

A student has a savings account earning 9 simple interest She must pay 1600 for first semester tuition by September 1 and 1600 for second semester tuition by January 1 How much must she earn in the summer by September 1 to pay the first semester bill on time and still have the remainder of her summer earnings grow to 1600 between September 1 and January 1 Round your answer to the nearest cent

For the given functions find fog x and gof x and the domain of each 5 1 4x f x fog x gof x 1 g x X O C Simplify your answer Simplify your answer What is the domain of f o g OA 0 0 U 0 00 OC 0 U 0 4 U 4 00 What is the domain of g o f O A 0 U 17 00 0 0 U 0 1 U 14 O B 0 4 U 4 00 OD 4 U 4 0 U 0 00 OB 0 0 U 0 00 OD 0 4 U 4 00

Analyze the polynomial function f x x 0 3x 1 3677x 0 38229 Complete parts a through h The domain of the function is 0 00 Type your answer in interval notation The range of the function is 0 00 Type your answer in interval notation h Use the graph to determine where the function is increasing and where it is decreasing On which interval s is the function increasing Round the endpoints to two decimal places as needed Select all that apply A 0 78 C 0 58 00 E 0 39 B 0 88 00 D 0 78 0 58 F 0 88 0 39 h

At the movie theatre child admission is 5 10 and adult admission is 8 90 On Tuesday 151 tickets were sold for a total sales of 1123 50 How many child tickets were sold that day Number of child tickets X S

Saving At the movie theatre child admission is 5 10 and adult admission is 8 90 On Tuesday 151 tickets were sold for a total sales of 1123 50 How many child tickets were said that day

A Web music store offers two versions of a popular song The size of the standard version is 2 5 megabytes MB The size of the high quality version is 4 3 MB Yesterday there were 1340 downloads of the song for a total download size of 4718 MB How many downloads of the high quality version were there Number of high quality version downloads 5

Consider the following relation x 5 y 4 Step 1 of 2 Find four points contained in the inverse Express your values as an integer or simplified fraction Answer D C D C P C

r x x 4 Step 2 of 2 Determine the domain and range of the original function Express your answer in interval notation Answer 2 Points Show Work Domain Range Styles Format

Consider the following functions Step 2 of 2 Find the formula for if necessary Answer 4 Points Prev Show Work i BI UT 1 x x and simplify your answer Then find the domain for f x 4x and g x x 2 x FE 29 Domain Styles Format 6 x Round your answer to two decimal plac Keypas Keyboard Shortcu F

Consider the following function Step 4 of 4 Graph the parabola Answer 2 Points Prev Keyboard Points can be moved by dragging or using the arrow keys Points whose positions are related to a moved point will be updated automatical lines or curves will be drawn once all required points are plotted and will update whenever a point is moved Enable Zoom Pan 10 g x x 4 4 5 2012 5 X

Find the sum of the first 194 terms of the arithmetic sequence 15 13 11

Consider the following arithmetic sequence 9 3 a Identify d and a d a1 b Write the next three terms a4 25 26 6

Find the 100th term of the arithmetic sequence with first term 9 and sixth term 19

Write the first five terms of the sequence whose nth term is a 1 n a a2 11 B a3 a 25 11 11

Find the requested value and tell what the other numbers represent a Find r 250 1 000 7 8 Enter the rate as a decimal r Identify the following interest principal time b Find P 8 640 P P 0 04 2 P Identify the following Enter the rate as a decimal future value rate

Next question You can retry this question below For each function determine the long run behavior x 1 x 2 x 1 x 2 x 1 x 2 has No horizontal asymptote X has a Horizontal asymptote at y 0 X has a Horizontal asymptote at y 1 X

Find a polynomial of degree 3 with only real coefficients and zeros of 7 1 and 0 for which f 2 1 Choose the correct polynomial of degree 3 with only real coefficients and zeros of 7 1 and 0 for which f 2 1 OA f x OB f x 6 x x x3 7 30x 1x 30 5 6 3 O c f x 1 x 2 x 6 5 7 OD f x 1 30 3 to 115 N 7 X 30

Use the factor theorem and synthetic division to decide whether the second polynomial is a factor of the first x3 7x2 7x 15 x 5 Is x 5 a factor of x3 7x2 7x 15 O Yes O No

Divide using synthetic division x5 5x 4x 3x 9x 7 X 4 x5 5x 4x 3x 9x 7 0 X 4 Simplify your answer Use integers or fractions for any numbers in not factor

writing a ratio 2 Why do you need to find the number that is halfway between 0 and 1 So You can know how many Cieps of flour goes with legg How could you find the number that is between 0 and 1 11 1 1 2 4 How many cups of flour does Max need to use if he has just 1 egg Show your work Write the ratio that compares 1 cups of flour to 2 eggs cups of flour eggs 2 6 Write and simplify a division expression to find the number of cups of flour Max needs to use if he has just 1 egg 2 360 d So would be the answer 3 7 The unit rate is 37 The number of cups of flour is Explain how to find a unit rate find a unit rate You have to divide in times times the number of eggs Try It Use what you just learned about finding a unit rate to solve these problems Show your work on a separate sheet of paper Use the information in the recipe on the previous page 9 If Max has only one egg how much butter will he need no cup of flour how much vanilla will he need

32 Since birth Hadley has had a savings account that started at 4000 and has been growing at a rate of 10 per year The amount of money in the account can be modeled by the equation y P 1 10 where y is the value of the account a is the number of years and P was the original deposit amount Is it possible for Hadley s account to grow to 6470871343 1 within Hadley s lifetime Hint try to figure out the bounds of the parameter O yes no None of these is correct

26 What does a equal in the solution of the system of equations below 2x 6y 2z 2 y 32 5 y 2z 0 O 1 O 9 O 4 0 2 M

7g 35 28 Simplify 20 49 O OF 07 9 O 0 7 g 5 49 20 C 7 g 5 4 this equation is already in simplest form

A guy wire 1766 feet long is attached to the top of a tower When pulled taut it touches level ground 747 feet from the base of the tower What angle does the wire make with the ground Express your answer using degree measure rounded to one decimal place degrees

17 Find the three arithmetic means between 24 and 28 24 28 O8 1 11 O 11 2 15 Jhy 21 O 6 4 O12 0 13 O None of these are correct 1 12 Simplify the following expression

3 Identify the function given y 5 12 O absolute value function O direct variation function O constant function Ostep function

3 Third Avenue Value Fund has a net asset value of 3 95 Bonnie Prince invested 8 250 If the loading rate is 5 front loaded how many shares did Bonnie purchase

Graph the function f x log x You can only graph integer points for example you cannot plot the point The red point can be moved above and below the x axis Do not move the point off of the graph as you will not be able to click on it again 1 Provide your answer below 3 0 2 3 4 5 6 7 8 9

The volume of a rectangular solid can be written as V LWH where L is the length of the solid W is the width and H is the height A box of cereal has a width of 2 inches Its height is 4 inches longer than its length If the volume of the box is 234 cubic inches what are the length and height of the box The length of the box is BUD inches

Points 0 of 10 The width of the floor of the shed is ft The floor of a shed has an area of 88 square feet The floor is in the shape of a rectangle whose length is 5 feet less than twice the width Find the length and the width of the floor of the shed Save

X 10 Fill in each blank with the appropriate number Use to denote a fraction if needed b X 3 4 2 2 5 Write your response here Write your response mere

Click on the center of the graph of the function f x 6 2 4 A B C D